However I cannot alter the data, it's for a lab. Would it be logical to try to fit a sigmoid function (f(x)=a/(b+e^-x)) to the data? If so, how would I find and input the parameters? Thank you for your help on this matter

I initially proposed the 0.1*x. That was estimated by calculating the slope between x==3 and x==18, subtracting that from the original data, plotting the result and concluding that was close enough. I tried small variations in that and it didn't seem to make a lot of difference.

Yes -- I followed Bill on 0.1 x, and with that FindFit actually found the breakpoint value of x0. But inspection of the data plot and the function pretty well shows the break in the exponential to be at about 20. (Note that Vitaliy used (x0,20}, but I didn't assign a start to x0, but I fixed the 0.1. I suspect making estimates of this sort of thing is important where parameter values control fluxuations that extreme.

I would like to propose a different way of doing the non-linear fitting using Quantile regression with B-splines. The advantages of the approach are that it does not need guessing of the fit functions and it requires less experimentation.

Hi Everyone,I have a new set of data I am trying to fit a function to.{{0, 0}, {5, 0.3}, {10, 0.6}, {15, 0.25}, {20, 0.14}, {25, 0.1}, {30, 0.05}, {35, 0.02}, {40, 0.01}}I believe it to be Lognormal but cannot seem to fit a function to it.Thanks in advance.

I did use EDA, it works just like NonlinearRegression but adds in the residual plot and provides a little more information. I figured out what the equation is, the first number provided after the parameter is the value used in the equation, I do not know what the second number represents but I have a feeling it is related to the error of the function. Thanks again for your help.

Thanks Ugo! How would I interpret the fitted function? If it is a piecewise function as I suspect, how would I integrate this? I took the top line after the bracket and graphed it from x>0 to x=40 but the function reached its apex around f(x)=.09. Thanks in advance!